📚 Light: Key Exam Points for IB & WJEC Science | 光：IB与WJEC科学考点精讲
Light is a fundamental topic in both IB and WJEC science curricula, encompassing wave optics, geometric optics, and the nature of electromagnetic radiation. Mastering the key principles of reflection, refraction, interference, and the electromagnetic spectrum not only secures high marks in examinations but also builds a deep understanding of how light interacts with the world. This revision guide systematically walks you through the essential concepts, equations, and real-world applications, providing bilingual explanations to reinforce learning.
光是IB和WJEC科学课程中的核心主题，涵盖波动光学、几何光学以及电磁辐射的本质。掌握反射、折射、干涉和电磁波谱的关键原理，不仅能在考试中取得高分，也能深刻理解光与世界的相互作用。这篇复习指南系统地梳理了基本概念、重要方程和实际应用，并提供双语讲解以强化学习效果。
1. Nature of Light and Electromagnetic Waves | 光的本质与电磁波
Light is a transverse electromagnetic wave that can travel through a vacuum at a speed of c = 3.00 × 10⁸ m s⁻¹. It exhibits wave-particle duality, but at the IB and WJEC level we primarily treat it as a wave. The relationship between speed (c), frequency (f), and wavelength (λ) is given by the wave equation c = fλ. Visible light occupies only a tiny fraction of the whole electromagnetic spectrum, with wavelengths ranging approximately from 400 nm (violet) to 700 nm (red).
光是一种横电磁波，能在真空中以 c = 3.00 × 10⁸ 米/秒的速度传播。它表现出波粒二象性，但在 IB 和 WJEC 阶段我们主要将其视为波。速度 (c)、频率 (f) 和波长 (λ) 之间的关系由波动方程 c = fλ 给出。可见光仅占整个电磁波谱的极小部分，波长范围约为 400 纳米（紫光）至 700 纳米（红光）。
All electromagnetic waves share common properties: they can be reflected, refracted, diffracted, and polarised. They transfer energy without transferring matter. The energy of a photon is directly proportional to its frequency, E = hf, but detailed photon calculations are more prominent in higher-level quantum physics. For most optics topics, the wave model is sufficient.
所有电磁波具有共同特性：它们可以被反射、折射、衍射和偏振。它们传递能量而不传递物质。光子的能量与其频率成正比，E = hf，不过详细的光子计算在更高层次的量子物理中更为突出。在大多数光学课题中，波动模型已足够。
2. Reflection and Plane Mirrors | 反射与平面镜
The law of reflection states that the angle of incidence (θᵢ) equals the angle of reflection (θᵣ), both measured from the normal to the surface. This is written as θᵢ = θᵣ. When you draw ray diagrams, always use a ruler and indicate the normal as a dashed line. The image formed by a plane mirror is virtual, upright, laterally inverted, and the same size as the object, located as far behind the mirror as the object is in front.
反射定律表明，入射角 (θᵢ) 等于反射角 (θᵣ)，两者均从法线量起。可写作 θᵢ = θᵣ。绘制光路图时务必使用直尺，并将法线画为虚线。平面镜所成的像是虚像、正立、左右颠倒、与物体等大，且像在镜后的距离与物体在镜前的距离相等。
In IB and WJEC exams, you might be asked to construct ray diagrams for extended objects or to explain how the eye perceives an image in a mirror. Remember that only two rays are necessary: one parallel to the principal axis that reflects as if coming from the focal point (for curved mirrors), but for a plane mirror a simple ray incident at the mirror and its reflection obeying the law are sufficient. Virtual rays are drawn as dotted lines behind the mirror.
在 IB 和 WJEC 考试中，你可能需要为扩展物体构建光路图，或解释眼睛如何看到镜中的像。请记住，只需画两条光线：对于曲面镜，需要一条平行于主轴并从焦点反射的光线；而对于平面镜，只需画出入射光线及其遵守反射定律的反射光线即可。虚光线在镜后用虚线表示。
3. Refraction and Snell’s Law | 折射与斯涅尔定律
Refraction occurs when light passes from one transparent medium into another of different optical density, causing a change in speed and direction. The refractive index n of a medium is defined as n = c / v, where v is the speed of light in the medium. Snell’s law relates the angles and refractive indices: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are measured from the normal. When light enters a denser medium, it bends towards the normal; when it enters a less dense medium, it bends away from the normal.
当光从一种透明介质进入另一种光密度不同的介质时会发生折射，导致速度和方向改变。介质的折射率 n 定义为 n = c / v，其中 v 是光在该介质中的速度。斯涅尔定律将角度和折射率联系起来：n₁ sin θ₁ = n₂ sin θ₂，其中 θ₁ 和 θ₂ 从法线量起。当光进入光密介质时，向法线偏折；进入光疏介质时，远离法线偏折。
Refractive indices are dimensionless numbers. For example, air ≈ 1.00, water ≈ 1.33, crown glass ≈ 1.50. When light travels from air into glass, it slows down and the wavelength decreases, but the frequency remains constant. You may be required to calculate the angle of refraction or the critical angle in both IB and WJEC problems, often using a scientific calculator for sin⁻¹ functions.
折射率是没有单位的数值。例如，空气约 1.00，水约 1.33，冕牌玻璃约 1.50。当光从空气进入玻璃时，速度减慢，波长减小，但频率保持不变。在 IB 和 WJEC 题目中，你可能需要计算折射角或临界角，经常使用科学计算器的 sin⁻¹ 功能。
4. Total Internal Reflection | 全内反射
Total internal reflection (TIR) occurs when light travels from a denser medium to a less dense medium at an angle of incidence greater than the critical angle θc. The critical angle is given by sin θc = n₂ / n₁, where n₁ > n₂. At the critical angle, the refracted ray runs along the boundary (angle of refraction = 90°). For angles greater than θc, all light is reflected internally, and no refraction occurs.
全内反射 (TIR) 发生在光从光密介质进入光疏介质、且入射角大于临界角 θc 时。临界角由 sin θc = n₂ / n₁ 给出，其中 n₁ > n₂。在临界角处，折射光线沿交界面传播（折射角 = 90°）。当入射角大于 θc 时，所有光线均被内部反射，不发生折射。
TIR is the principle behind optical fibres, which are widely used in telecommunications and medical endoscopy. An optical fibre consists of a core with a high refractive index surrounded by a cladding of lower refractive index. Light entering at one end bounces inside the core via multiple total internal reflections, emerging at the other end with very little loss. In exams, you may need to explain the conditions for TIR and its advantages in fibre optics.
全内反射是光纤背后的原理，光纤广泛应用于通信和医用内窥镜。光纤由高折射率的纤芯和低折射率的包层组成。光从一端进入后，通过多次全内反射在纤芯内弹跳，最终以极低损耗从另一端射出。考试中，你可能需要解释 TIR 的条件及其在光纤中的优势。
5. Lenses and Image Formation | 透镜与成像
There are two main types of thin lenses: converging (convex) and diverging (concave). A converging lens is thicker in the middle and brings parallel rays to a real focus; a diverging lens is thinner in the middle and causes parallel rays to appear to diverge from a virtual focus. The thin lens equation is 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance. Magnification M is given by M = v/u = image height / object height.
薄透镜主要有两种类型：会聚透镜（凸透镜）和发散透镜（凹透镜）。会聚透镜中间厚，能使平行光线会聚在实焦点上；发散透镜中间薄，使平行光线看似从虚焦点发散出来。薄透镜方程为 1/f = 1/u + 1/v，其中 f 为焦距，u 为物距，v 为像距。放大率 M 由 M = v/u = 像高/物高 给出。
In IB and WJEC sign conventions, real images have positive v, virtual images have negative v; converging lenses have positive f, diverging lenses have negative f. You must be able to construct accurate ray diagrams using at least two of the three standard rays: (1) a ray parallel to the principal axis, which passes through the focal point on the other side; (2) a ray passing through the centre of the lens, which continues undeviated; (3) a ray passing through the focal point on the same side, which emerges parallel to the axis. For a diverging lens, the focal point is on the same side as the object.
在 IB 和 WJEC 符号法则中，实像的 v 为正，虚像的 v 为负；会聚透镜的 f 为正，发散透镜的 f 为负。你必须能够使用三条标准光线中的至少两条来绘制准确的光路图：(1) 平行于主轴的光线，通过另一侧的焦点；(2) 通过透镜中心的光线，方向不变；(3) 通过同侧焦点的光线，折射后平行于主轴。对于发散透镜，焦点与物体在同一侧。
6. Wave Nature: Interference and Diffraction | 波动性：干涉与衍射
Light exhibits interference and diffraction, confirming its wave nature. Interference occurs when two coherent waves superpose, producing regions of constructive interference (bright fringes) and destructive interference (dark fringes). For constructive interference, the path difference must be an integer multiple of the wavelength: Δpath = mλ, where m = 0, 1, 2, … For destructive interference, the path difference is an odd multiple of half wavelengths: Δpath = (m + ½)λ.
光表现出干涉和衍射现象，证实了其波动性。干涉发生在两列相干波叠加时，产生相长干涉（明纹）和相消干涉（暗纹）。相长干涉要求光程差为波长的整数倍：Δpath = mλ，其中 m = 0, 1, 2, …；相消干涉要求光程差为半波长的奇数倍：Δpath = (m + ½)λ。
Diffraction is the spreading of waves around obstacles or through slits. The amount of diffraction increases when the wavelength is comparable to the aperture size. A single slit produces a central maximum and a series of minima at angles given by a sin θ = nλ, where a is the slit width and n = 1, 2, 3, … (Note: n starts from 1 for minima). This concept is vital for understanding the envelope pattern in double-slit experiments.
衍射是波在障碍物周围或穿过狭缝时发生的扩展现象。当波长与孔径尺寸可比拟时，衍射效应更显著。单缝产生中央明纹和一系列极小值，角度由 a sin θ = nλ 给出，其中 a 是缝宽，n = 1, 2, 3, …（注意：极小值从 n=1 开始）。这一概念对于理解双缝实验中的包络线图样至关重要。
7. Double-Slit Experiment | 双缝实验
Young’s double-slit experiment provides clear evidence for the wave nature of light. Coherent light illuminates two narrow slits separated by a distance d. On a screen placed at a distance L (where L >> d), an interference pattern of equally spaced bright and dark fringes is observed. The fringe spacing (distance between adjacent bright fringes) is Δx = λL / d. This formula allows calculation of the wavelength of light if Δx, L, and d are known.
杨氏双缝实验为光的波动性提供了明确证据。相干光照射两条相距 d 的狭缝，在距离 L 远（L >> d）的屏幕上可观察到等间距的明暗条纹干涉图样。条纹间距（相邻明纹之间的距离）为 Δx = λL / d。利用该公式，若已知 Δx、L 和 d，便可计算出光的波长。
Bright fringes occur at angles satisfying d sin θ = mλ, with m = 0, 1, 2, …, and dark fringes at d sin θ = (m + ½)λ. The central maximum (m = 0) is the brightest. The intensity of the fringes is modulated by the single-slit diffraction pattern, which students should sketch accurately in exams. Using a laser as a coherent source yields the sharpest fringes; white light produces a central white fringe with coloured fringes on either side because each wavelength has a different spacing.
明纹满足 d sin θ = mλ，其中 m = 0, 1, 2, …；暗纹满足 d sin θ = (m + ½)λ。中央明纹 (m = 0) 最亮。条纹强度受单缝衍射图样的调制，学生在考试中应准确绘制。使用激光作为相干光源可获得最清晰的条纹；白光则产生中央白色明纹，两侧为彩色条纹，因为不同波长的间距不同。
8. Diffraction Gratings | 衍射光栅
A diffraction grating consists of a large number of equally spaced parallel slits (lines). It produces much sharper and brighter maxima than a double slit, making it ideal for precise wavelength measurement. The condition for principal maxima is d sin θ = nλ, where d is the grating spacing (the distance between adjacent lines, often given as 1/N where N is lines per metre), n is the order number (0, 1, 2, …), and θ is the angle between the incident beam and the diffracted beam.
衍射光栅由大量等间距平行刻线（狭缝）组成。它能产生比双缝更锐利、更明亮的极大值，因此非常适合精确测量波长。主极大的条件为 d sin θ = nλ，其中 d 是光栅间距（相邻刻线之间的距离，常表示为 1/N，N 为每米刻线数），n 是级数 (0, 1, 2, …)，θ 是入射光束与衍射光束之间的夹角。
In a typical experiment, a laser of known wavelength is directed at a grating, and the distances from the central spot to the nth-order spot are measured. Using tan θ = x / L and the small-angle approximation (if appropriate), you can determine d or verify λ. Diffraction gratings are used in spectrometers to analyse light from stars, to identify elements, and in CD/DVD technology. Students must be able to explain why a grating produces sharper fringes and how increasing the number of lines improves resolution.
在典型实验中，将已知波长的激光照射到光栅上，测量中央亮斑到第 n 级亮斑的距离。利用 tan θ = x / L 以及（在条件适合时）小角度近似，可以求出 d 或验证 λ。衍射光栅被用于光谱仪中分析恒星光芒、识别元素，也应用于 CD/DVD 技术。学生需能解释为何光栅能产生更锐利的条纹，以及增加刻线数如何提高分辨率。
9. Electromagnetic Spectrum and Visible Light | 电磁波谱与可见光
The electromagnetic (EM) spectrum is arranged by wavelength and frequency. From longest wavelength to shortest, the main regions are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All EM waves travel at the speed of light in a vacuum. Visible light is the only part detectable by the human eye, with wavelengths roughly from 4.0 × 10⁻⁷ m to 7.0 × 10⁻⁷ m.
电磁波谱按波长和频率排列。从长波到短波的主要区域依次是：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。所有电磁波在真空中均以光速传播。可见光是唯一人眼可探测的部分，波长大约从 4.0 × 10⁻⁷ 米 到 7.0 × 10⁻⁷ 米。
Each region has distinct properties and applications. For example, radio waves are used in communication, microwaves in cooking and radar, infrared in remote controls and thermal imaging, ultraviolet in sterilisation and detecting forged bank notes, X-rays in medical imaging, and gamma rays in cancer treatment. The energy of EM radiation increases with frequency: gamma rays are the most energetic and penetrating, while radio waves are the least.
每个区域都有独特的性质和应用。例如，无线电波用于通信，微波用于烹饪和雷达，红外线用于遥控和热成像，紫外线用于消毒和检验伪钞，X 射线用于医学成像，伽马射线用于癌症治疗。电磁辐射的能量随频率增加而增大：伽马射线能量最高、穿透力最强，而无线电波最低。
| Region 区域 | Wavelength Range 波长范围 | Frequency Range 频率范围 |
|---|---|---|
| Radio waves 无线电波 | > 0.1 m | < 3 × 10⁹ Hz |
| Microwaves 微波 | 1 mm – 0.1 m | 3 × 10⁹ – 3 × 10¹¹ Hz |
| Infrared 红外线 | 700 nm – 1 mm | 4.3 × 10¹⁴ – 3 × 10¹¹ Hz |
| Visible 可见光 | 400 – 700 nm | 4.3 × 10¹⁴ – 7.5 × 10¹⁴ Hz |
| Ultraviolet 紫外线 | 10 – 400 nm | 7.5 × 10¹⁴ – 3 × 10¹⁶ Hz |
| X-rays X射线 | 0.01 – 10 nm | 3 × 10¹⁶ – 3 × 10¹⁹ Hz |
| Gamma rays 伽马射线 | < 0.01 nm | > 3 × 10¹⁹ Hz |
10. Dispersion, Colour and Polarisation | 色散、颜色与偏振
Dispersion is the splitting of white light into its constituent colours when it passes through a prism. This happens because the refractive index of glass varies with wavelength; shorter wavelengths (violet) are refracted more than longer wavelengths (red). The sequence of colours is red, orange, yellow, green, blue, indigo, violet (ROYGBIV). Rainbows are a natural example of dispersion through water droplets.
色散是指白光通过棱镜时分解为其组成颜色的现象。这是因为玻璃的折射率随波长而变化；波长越短（紫光）比长波长（红光）折射得更多。颜色顺序为红、橙、黄、绿、蓝、靛、紫。彩虹是阳光通过水滴发生色散的自然实例。
The colour of an opaque object depends on which wavelengths it reflects. A red apple absorbs all colours except red, which it reflects. A black object absorbs all visible wavelengths, while a white object reflects them all. In filters, a red filter transmits only red light and absorbs the rest. Mixing of coloured light (additive mixing) follows different rules than mixing of pigments (subtractive mixing). The primary additive colours are red, green, and blue.
不透明物体的颜色取决于它反射哪些波长的光。红苹果吸收除红光外的所有颜色，只反射红色；黑色物体吸收所有可见波长，白色物体则全部反射。对于滤光片，红色滤光片只透过红光，吸收其余颜色。彩色光的混合（加法混色）与颜料的混合（减法混色）遵循不同的规则。加法三原色是红、绿、蓝。
Polarisation is evidence that light is a transverse wave. Unpolarised light vibrates in all planes perpendicular to the direction of travel. A polarising filter transmits only the component of the wave oscillating in a specific plane. When unpolarised light passes through an ideal polariser, its intensity is halved. If a second polariser (analyser) is placed after the first, the transmitted intensity is given by Malus’s law: I = I₀ cos² θ, where θ is the angle between the transmission axes of the two polarisers. Polarisation has applications in LCD screens, photography to reduce glare, and stress analysis.
偏振证明光是横波。非偏振光在所有垂直于传播方向的平面上振动。偏振滤光片只透过在特定平面内振动的波分量。当非偏振光通过一个理想偏振片后，其强度减半。如果在第一个偏振片后再放置一个偏振片（检偏器），透射光强由马吕斯定律给出：I = I₀ cos² θ，其中 θ 为两个偏振片透射轴之间的夹角。偏振在液晶显示屏、摄影中减弱眩光以及应力分析中都有应用。
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